Ellmenreich, J., Giacomini, M., Huerta, A., & Lederer, P. L. (2026). Characteristic boundary conditions for hybridizable discontinuous Galerkin methods. Journal of Computational Physics, 548, Article 114565. https://doi.org/10.1016/j.jcp.2025.114565
In this work we introduce a novel approach to generalized characteristic relaxation boundary conditions (GRCBCs). Our method requires the user to specify Courant-Friedrichs-Lewy (CFL) number like relaxation factors and recovers commonly used boundary conditions for compressible flow in the context of Hybridizable Discontinuous Galerkin (HDG) methods as a special case. GRCBCs belong to the class of characteristic boundary conditions (CBCs), which are based on the characteristic decomposition of the compressible Euler equations and are designed to prevent the reflection of waves at the domain boundaries. We extend the concept of CBCs within the framework of HDG methods, encompassing both the novel GRCBCs and the well-established Navier-Stokes characteristic boundary conditions (NSCBCs). We show the effectiveness of the proposed method for weakly compressible flows through a series of numerical experiments by comparing the results with common boundary conditions in the HDG setting and reference solutions available in the literature. In particular, HDG with CBCs shows superior performance minimizing the reflection of vortices at artificial boundaries, for both inviscid and viscous flows, due to the inclusion of appropriate tangential and/or viscous contributions into the boundary conditions.
